ELEMEMTARY ALGORITHMICS INTRODUCTION

We are constantly involved in solving problem. The problems may concern our survival in a competitive and hostile environment, may concern our curiosity to know more and more of various facets of nature or may be about any other issues of interest to us. Problem may be a state of mind of a living being, of not being satisfied with some situation. However, for our purpose, we may take the unsatisfactory/ unacceptable/ undesirable situation itself, as a problem.

Arrange the following growth rates in increasing order

Question: Arrange the following growth rates in increasing order : 0 (4n), 0(n4), 0(1), 0(n3 logn), where '0' denotes 'big O'.

Solurion:

Using Insertion Sort or Bubble Sort

Question :Using Insertion Sort or Bubble Sort 
(state before starting the solution, which algorithm for sorting, you are using),
sort the following sequence of integers in decreasing order :
85 36 34 109 49 36

Solution: 

Let Lx denote floor function of x and Fx denote ceiling function of x. Find values of :

Question:  Let Lx denote floor function of x and Fx  denote ceiling function of x. Find values of :

  


Solution:

State any four characteristics of an algorithm, with an appropriate examples.

Question :State any four characteristics of an algorithm, with an appropriate examples.

Solution:

The Four - Colour Problem & The Fermat's Last Theorem

Question: State and describe any one of the following two problems :
(i)The Four - Colour Problem
(ii)The Fermat's Last Theorem


Solution:

Explain the relation/difference between a problem and its instance through an example of each.

Question : Explain the relation/difference between a problem and its instance through an example of each.

Solution: